Not as much as with other games thanks to the wonder of procedural generation Braben talks about this in an early video). After all, Frontier with its vector graphics and generated galaxy fit on a 720 kB floppy disc.

For what it's worth, the first Alpha install size was apparently around 1.2GB, though that was just the flight model part. The Alpha 4 is supposed to weigh 2-3 GB.

Dirtbox wrote:
Has no one played any of the previous Elites? All this stuff was in those as well, albeit without the extra pretty.

Kind of. BBC Elite fitted 8 galaxies on one side of a 40-track 100k floppy, and still had room for the game. But those were 2d galaxies, and looked a lot smaller than the one in that vid. There were still a few unvisitable planets except using hacks, and in 3d without the right algorithm you'd have far many more I suspect.

Edit: And Geoff Crammond's Sentinel still beat it, for having 10000 3d levels, and I got that on a bootleg floppy with 7 other games on it.